ON BEST SIMULTANEOUS APPROXIMATION

The problem is considered of best approximation of finite number of fu nctions simultaneously. For a very general class of norms, characteriz ation results are derived. The main part of the paper is concerned wit h proving uniqueness and strong uniqueness theorems. For a particular subclass, which includes the important special case of the Chebyshev n orm, a characterization is given of a uniqueness element. (C) 1997 Aca demic Press.